152 Chapter l4 Bootstrap Methods and Permutation Tests
With the sample in list L1 , we can execute the BOOT program to bootstrap the sample
mean. In this case, we enter 0 for CONF. INTERVAL? because we are only interested
here in the bootstrap distribut
I42 Chapter [3 Two Way Analysis of Variance
To create the means plot, use Matr>Li st from the Matrix Math menu to create lists
to plot. You need to specify as many lists as there are columns in [B]. Next, input a
column containing values 1, 2, and 3 in L4
First Steps in Using the Bootstrap [5|
in mean reading scores for the two teaching methods of (8.177, 11.732). Since the
interval does not contain 0, we have evidence that the directed reading activities help
students reading ability.
PPEIP'IEUUTF'FIIR EI
Inference for One-Way Analysis of Variance I33
The second assumption is that the data come from Normal populations. We could do a
Normal plot for each type of ower, but in this case side-by-side boxplots are a good
idea. Were looking for indications of sk
The Bootstrap ldea 145
14.1 The Bootstrap Idea
We first provide a T1 calculator program that performs resampling on a previously
obtained random sample. Before executing the BOOT program, enter the random
sample into list L1. Then bring up the program and
I34 Chapter [2 One Way Analysis of Variance
We can test any pair of species for equality of mean very quickly using 2-SampTTest,
but need to pay attention to p-values that might cause problems due to multiple
comparisons. Since one of the assumptions of A
Inference for Multiple Regression I27
Example 11.2 More Grade Predictions. Use the preceding regression model to predict
the GPA ofa student with HSM = 8, H88 = 7, and HSE = 10.
Tl83/84 Solution. Rerun program MULREG, but this time press to answer YES
to
Simple Linear Regression I 17
From condence interval for the slope, we see that we are 95% confident the average cost
per square foot in Augusta at that time (for houses of this type) was somewhere between
$9.43 and $59.16. Based on this sample, the avera
148 Chapter 14 Bootstrap Methods and Permutation Tests
Condence Interval for a Trimmed Mean
Next, we demonstrate a program that will compute a bootstrap t confidence interval for a
trimmed mean (where x% of data at the top and bottom are deleted or trimme
Inference for Two-Way ANOVA I39
The ANOVAZW Program
PROGRAMzANOVAZW
Disp DATA IN [A]"
Disp ","FACTOR A :
ROWS?II,H1=YESVV3II2=NOH,HH
Repeat F #0: getKeymF :End
If F:92:[A]T:ST0v [A]
Input NOP B LEVELS=",B
djm([A]) -L8A: LGA (2) -A: LBA
(1 )fB-N
1 (HERB
cf
CHAPTER
12
One-Way
Analysis of
Variance
12.1
12.2
Inference for One-Way Analysis of
Variance
Comparing the Means
Introduction
Just as a chi-squared test can be seen as an extension of the two-proportion test, One-way
Analysis of Variance (ANOV
CHAPTER
Y
Two-Way
Analysis of
Variance
13.1 Plotting Means
13.2 Inference for Two-Way ANOVA
Introduction
Two-way analysis of variance is really best performed with a full statistical package on a
computer. However, with a fairly lengthy program,
First Steps in Using the Bootstrap 147
Example 14.3 More Guinea Pig Survival. Lets return to the 20 guinea pig survival
times from Example 14.1.
(a) What is the bootstrap estimate of the bias?
(b) Give the 95% bootstrap tconfidence interval for ,u .
(0) G
Comparing the Means 135
Example 12.2 Workplace Safety. The table below gives the summary data on safety
climate index (SCI) as rated by workers during a study on workplace safety. Apply the
ANOVA test and give the pooled deviation, the value of r2, the Fs
Inference for Two-Way ANOVA I41
Perform twoway ANOVA on the data regarding the main effects and interaction, then
plot the means and examine the plot.
TI83/84 Solution. Enter the data into matrix [A]. (Hint: it may sometimes be easier to
enter data into l
CHAPTER
14
naval, liai-
cfw_Eli-4:931
cfw_IE-:3:1|EI:-E
Bootstrap Methods
and Permutation Tests
14.1 The Bootstrap Idea
14.2 First Steps in Using the Bootstrap
14.3 How Accurate Is a Bootstrap Distribution?
14.4 Bootstrap Confidence Intervals
14.5 S
Inference for Multiple Regression 123
11.1 Inference for Multiple Regression
The MULREG program below computes the regression coefficients and an ANOVA
table for the multiple linear regression model y, = o+xx1+.+kxk. The program
stores the regression coef
First Steps in Using the Bootstrap I49
The BOOTTRIM Program
Program:BOOTTRIM
:dim(L l )-N
:Disp "NO. OF RESAMPLES"
:lnput B
:Disp "DEC. TRIM AMT?
:Input M
:Disp "CONF. LEVEL"
:Input R
:"tcdf(0,X,N- 1)" -Y1
:solve(Yl R/2,X,2) -Q
:int(M*N)+l-L
:int(l-M)*N)
126 Chapter I I Multiple Regression
The program stores the computed regression coefficients and their associated statistics in
L1 through L4. In this case, our model becomes ,uGPA = 0.228 + 0.0397*HSM +
0.2424*HSS + 0.0852*HSE. The Standard errors are in
Inference for Multiple Regression I25
T 1-83/84 Solution. We use the model ,uGPA = [30 +[y1xHSM + zxfm + nggE, which is of
the form ,uY = o + xxl + zxz + 3x3. In this case, there are 24 sample points and four
variables. We must first enter the data into m
I30 Chapter I I Multiple Regression
bringing this command to the Home screen, enter the command
List>matr(L4,L5,L6, [A] ), Where [A] is retrieved from the MATRIX NAMES
menu.
HHHES ' EDIT ListrmatriLuaLsa MHTRIH[H]
ETlden 1 Hi LE=[H]) [335
E=Pand
2.
T": au
I 14 Chapter IO Inference for Regression
You are now asked for the confidence level. Here we want 90%, so enter .9. You are
now asked what x value we are interested in. Since we are interested in the intercept,
enter 0. Press to continue. We first find a
A Case Study 129
(a) Use a simple linear regression to predict assets using the number of accounts. Give
the regression equation and the results of the significance test for the regression
coefficient.
(b) Do the same using market share to predict assets.
Inference for Two-Way ANOVA I43
Unfortunately, the Tl89 does not create the cell means for you to create the means plot.
You can calculate these fairly easily, though. Enter four 1s in list 4, then four 23, then
four 3 5. These will correspond to the type